# Circle Corner

Written by Jerry Ratzlaff on . Posted in Plane Geometry

•  Circle corner (a two-dimensional figure) is a right triangle having acute vertices on a circle with the hypotenuse outside the circle.
• Chord is a line segment on the interior of a circle.
• Segment of a circle is an interior part of a circle bound by a chord and an arc.

## area of a Circle Corner formula

 $$\large{ A = \frac{a\;b \;-\; r \; L \;+\; c \; \left(r \;-\; h\right) }{2 } }$$

### Where:

 Units English Metric $$\large{ A }$$ = area $$\large{ft^2}$$ $$\large{m^2}$$ $$\large{ L }$$ = arc length $$\large{ft}$$ $$\large{m}$$ $$\large{ c }$$ = chord length $$\large{ft}$$ $$\large{m}$$ $$\large{ a, b }$$ = edge $$\large{ft}$$ $$\large{m}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$ $$\large{ h }$$ = segment height $$\large{ft}$$ $$\large{m}$$

## Arc Length of a Circle Corner formula

 $$\large{ L = r \; \Delta }$$

### Where:

 Units English Metric $$\large{ L }$$ = arc length $$\large{ft}$$ $$\large{m}$$ $$\large{ \Delta }$$ = angle $$\large{deg}$$ $$\large{rad}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$

## Chord Length of a Circle Corner formula

 $$\large{ c = a^2 \; b^2 }$$

### Where:

 Units English Metric $$\large{ c }$$ = chord length $$\large{ft}$$ $$\large{m}$$ $$\large{ a, b }$$ = edge $$\large{ft}$$ $$\large{m}$$

## Height of a Circle Corner formula

 $$\large{ h = r \; \left( 1 - cos \; \frac{\Delta}{2} \right) }$$

### Where:

 Units English Metric $$\large{ h }$$ = segment height $$\large{ft}$$ $$\large{m}$$ $$\large{ \Delta }$$ = segment angle $$\large{deg}$$ $$\large{rad}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$

## Perimeter of a Circle Corner formula

 $$\large{ p = a + b + L }$$

### Where:

 Units English Metric $$\large{ p }$$ = perimeter $$\large{ft}$$ $$\large{m}$$ $$\large{ L }$$ = arc length $$\large{ft}$$ $$\large{m}$$ $$\large{ a, b }$$ = edge $$\large{ft}$$ $$\large{m}$$

## Segment Angle of a Circle Corner formula

 $$\large{ \Delta = arccos \; \frac{ 2\;r^2 \;-\; c^2 }{2\;r^2} }$$

### Where:

 Units English Metric $$\large{ \Delta }$$ = segment angle $$\large{deg}$$ $$\large{rad}$$ $$\large{ c }$$ = chord length $$\large{ft}$$ $$\large{m}$$ $$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$ 